An Adaptive Finite Element Method for the LaplaceBeltrami Operator on Implicitly Defined Surfaces Academic Article uri icon

abstract

  • We present an adaptive finite element method for approximating solutions to the Laplace-Beltrami equation on surfaces in ℝ3 which may be implicitly represented as level sets of smooth functions. Residual-type a posteriori error bounds which show that the error may be split into a "residual part" and a "geometric part" are established. In addition, implementation issues are discussed and several computational examples are given. © 2007 Society for Industrial and Applied Mathematics.

author list (cited authors)

  • Demlow, A., & Dziuk, G.

publication date

  • January 1, 2007 11:11 AM